- #1
Bacle
- 662
- 1
Hi, Algebraists:
Say I'm given a group's presentation G=<X|R>, with
X a finite set of generators, R the set of relations. A couple of questions, please:
i)If S is a subset of G what condition must the generators of
S satisfy for S to be a subgroup of G ? I know there is a condition
that if for any a,b in S, then S is a subgroup of G if ab^-1 is in S, but
I am tryng to work only with the generating set.
ii) If A,B are known to be subgroups of G; G as above: what
condition do I need on the generators of A,B respectively,
in order to tell if A is a subgroup of G? Is inclusion enough?
Thanks.
Say I'm given a group's presentation G=<X|R>, with
X a finite set of generators, R the set of relations. A couple of questions, please:
i)If S is a subset of G what condition must the generators of
S satisfy for S to be a subgroup of G ? I know there is a condition
that if for any a,b in S, then S is a subgroup of G if ab^-1 is in S, but
I am tryng to work only with the generating set.
ii) If A,B are known to be subgroups of G; G as above: what
condition do I need on the generators of A,B respectively,
in order to tell if A is a subgroup of G? Is inclusion enough?
Thanks.